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The particular Something I had in mind here would be air bubbles that are pulled downwards against their buoyancy by a stream of water falling down a shaft. The work required to push those bubbles down must decrease energy somewhere else, so where does it come from? Is the stream's velocity reduced?

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    $\begingroup$ What are the alternatives? $\endgroup$
    – Bernhard
    Feb 18, 2013 at 14:11

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Entrainment works by the entraining medium giving momentum and energy to the entrained medium. The Wiki page on the injector pump should get you started.

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